From Blaschke--Santaló-type inequalities to uniform contractions
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917277825236992 |
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| author | Bezdek, Károly |
| author_facet | Bezdek, Károly |
| contents | In this short note, we establish Blaschke--Santaló-type inequalities for $r$-ball bodies. Building on these inequalities, we somewhat further extend earlier results on analogues of the Kneser--Poulsen conjecture concerning intersections of balls under uniform contractions in Euclidean $d$-space. As an immediate corollary, we obtain a proof of Alexander's conjecture for uniform contractions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15352 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | From Blaschke--Santaló-type inequalities to uniform contractions Bezdek, Károly Metric Geometry In this short note, we establish Blaschke--Santaló-type inequalities for $r$-ball bodies. Building on these inequalities, we somewhat further extend earlier results on analogues of the Kneser--Poulsen conjecture concerning intersections of balls under uniform contractions in Euclidean $d$-space. As an immediate corollary, we obtain a proof of Alexander's conjecture for uniform contractions. |
| title | From Blaschke--Santaló-type inequalities to uniform contractions |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2602.15352 |